LMFDB - Embedded newform 975.2.w.h.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-2.10121 + 0.563016i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.h.49.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563016 + 0.975173i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(-0.975173 + 0.563016i) q^{6} +(-1.42904 - 2.47517i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.563016 + 0.975173i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(-0.975173 + 0.563016i) q^{6} +(-1.42904 - 2.47517i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.66422 - 1.53819i) q^{11} +0.732051i q^{12} +(0.601205 - 3.55507i) q^{13} +3.21829 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.68905 + 0.975173i) q^{17} -1.12603 q^{18} +(-6.42652 + 3.71035i) q^{19} -2.85808i q^{21} +(3.00000 - 1.73205i) q^{22} +(-7.61457 - 4.39627i) q^{23} +(-2.66422 - 1.53819i) q^{24} +(3.12832 + 2.58784i) q^{26} +1.00000i q^{27} +(1.04613 - 1.81195i) q^{28} +(-3.34120 + 5.78712i) q^{29} -3.15276i q^{31} +(-1.95035 - 3.37810i) q^{32} +(-1.53819 - 2.66422i) q^{33} -2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(4.12603 - 7.14650i) q^{37} -8.35596i q^{38} +(2.29820 - 2.77818i) q^{39} +(2.87710 + 1.66109i) q^{41} +(2.78712 + 1.60915i) q^{42} +(-8.26772 + 4.77337i) q^{43} -2.25207i q^{44} +(8.57425 - 4.95035i) q^{46} -1.79759 q^{47} +(1.73205 - 1.00000i) q^{48} +(-0.584320 + 1.01207i) q^{49} -1.95035 q^{51} +(2.47388 - 0.920099i) q^{52} +10.6569i q^{53} +(-0.975173 - 0.563016i) q^{54} +(4.39627 + 7.61457i) q^{56} -7.42071 q^{57} +(-3.76230 - 6.51649i) q^{58} +(-4.17256 + 2.40903i) q^{59} +(3.13397 + 5.42820i) q^{61} +(3.07448 + 1.77505i) q^{62} +(1.42904 - 2.47517i) q^{63} +8.39230 q^{64} +3.46410 q^{66} +(-2.93927 + 5.09097i) q^{67} +(-1.23647 - 0.713876i) q^{68} +(-4.39627 - 7.61457i) q^{69} +(8.91942 - 5.14963i) q^{71} +(-1.53819 - 2.66422i) q^{72} +11.1101 q^{73} +(4.64605 + 8.04719i) q^{74} +(-4.70454 - 2.71617i) q^{76} +8.79254i q^{77} +(1.41529 + 3.80530i) q^{78} +11.0968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.23970 + 1.87044i) q^{82} -6.97707 q^{83} +(1.81195 - 1.04613i) q^{84} -10.7499i q^{86} +(-5.78712 + 3.34120i) q^{87} +(8.19615 + 4.73205i) q^{88} +(-0.0805845 - 0.0465255i) q^{89} +(-9.65857 + 3.59226i) q^{91} -6.43659i q^{92} +(1.57638 - 2.73037i) q^{93} +(1.01207 - 1.75296i) q^{94} -3.90069i q^{96} +(-2.39879 - 4.15483i) q^{97} +(-0.657963 - 1.13963i) q^{98} -3.07638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 4 * q^9	$ 8 q - 4 q^{4} + 4 q^{9} - 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} + 24 q^{22} - 24 q^{23} - 24 q^{26} + 12 q^{28} - 12 q^{29} + 4 q^{36} + 24 q^{37} + 4 q^{39} + 36 q^{41} - 12 q^{42} + 12 q^{43} - 48 q^{47} + 4 q^{49} + 12 q^{52} - 24 q^{57} + 12 q^{58} - 36 q^{59} + 32 q^{61} + 48 q^{62} - 16 q^{64} + 12 q^{67} + 36 q^{71} + 48 q^{73} + 24 q^{74} - 48 q^{76} + 12 q^{78} + 16 q^{79} - 4 q^{81} + 12 q^{82} - 12 q^{84} - 12 q^{87} + 24 q^{88} - 36 q^{89} - 12 q^{93} - 12 q^{94} - 36 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 4 * q^9 - 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 + 24 * q^22 - 24 * q^23 - 24 * q^26 + 12 * q^28 - 12 * q^29 + 4 * q^36 + 24 * q^37 + 4 * q^39 + 36 * q^41 - 12 * q^42 + 12 * q^43 - 48 * q^47 + 4 * q^49 + 12 * q^52 - 24 * q^57 + 12 * q^58 - 36 * q^59 + 32 * q^61 + 48 * q^62 - 16 * q^64 + 12 * q^67 + 36 * q^71 + 48 * q^73 + 24 * q^74 - 48 * q^76 + 12 * q^78 + 16 * q^79 - 4 * q^81 + 12 * q^82 - 12 * q^84 - 12 * q^87 + 24 * q^88 - 36 * q^89 - 12 * q^93 - 12 * q^94 - 36 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.563016	+	0.975173i	−0.398113	+	0.689551i	−0.993493	−	0.113893i	$-0.963668\pi$
$2$	−0.563016	+	0.975173i	−0.398113	+	0.689551i	0.595380	+	0.803444i	$0.297001\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.366025	+	0.633975i	0.183013	+	0.316987i
$5$		0			0
$5$		0			0
$6$	−0.975173	+	0.563016i	−0.398113	+	0.229850i
$7$	−1.42904	−	2.47517i	−0.540127	−	0.935527i	−0.998896	−	0.0469719i	$-0.985043\pi$
$7$	−1.42904	−	2.47517i	−0.540127	−	0.935527i	0.458769	−	0.888555i	$-0.348290\pi$
$8$	−3.07638			−1.08766
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.66422	−	1.53819i	−0.803293	−	0.463781i	0.0413283	−	0.999146i	$-0.486841\pi$
$11$	−2.66422	−	1.53819i	−0.803293	−	0.463781i	−0.844621	+	0.535364i	$0.820174\pi$
$12$			0.732051i			0.211325i
$13$	0.601205	−	3.55507i	0.166744	−	0.986000i
$13$	0.601205	−	3.55507i	0.166744	−	0.986000i
$14$	3.21829			0.860125
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	−1.68905	+	0.975173i	−0.409654	+	0.236514i	−0.690641	−	0.723198i	$-0.742672\pi$
$17$	−1.68905	+	0.975173i	−0.409654	+	0.236514i	0.280987	+	0.959712i	$0.409338\pi$
$18$	−1.12603			−0.265408
$19$	−6.42652	+	3.71035i	−1.47434	+	0.851213i	−0.999582	−	0.0289008i	$-0.990799\pi$
$19$	−6.42652	+	3.71035i	−1.47434	+	0.851213i	−0.474762	+	0.880114i	$0.657466\pi$
$20$		0			0
$21$		−	2.85808i		−	0.623685i
$22$	3.00000	−	1.73205i	0.639602	−	0.369274i
$23$	−7.61457	−	4.39627i	−1.58775	−	0.916686i	−0.993677	−	0.112272i	$-0.964187\pi$
$23$	−7.61457	−	4.39627i	−1.58775	−	0.916686i	−0.594070	−	0.804414i	$-0.702480\pi$
$24$	−2.66422	−	1.53819i	−0.543832	−	0.313982i
$25$		0			0
$26$	3.12832	+	2.58784i	0.613515	+	0.507518i
$27$			1.00000i			0.192450i
$28$	1.04613	−	1.81195i	0.197700	−	0.342427i
$29$	−3.34120	+	5.78712i	−0.620445	+	1.07464i	0.368958	+	0.929446i	$0.379715\pi$
$29$	−3.34120	+	5.78712i	−0.620445	+	1.07464i	−0.989403	+	0.145196i	$0.953619\pi$
$30$		0			0
$31$		−	3.15276i		−	0.566252i	−0.959083	−	0.283126i	$-0.908629\pi$
$31$		−	3.15276i		−	0.566252i	0.959083	−	0.283126i	$-0.0913714\pi$
$32$	−1.95035	−	3.37810i	−0.344776	−	0.597169i
$33$	−1.53819	−	2.66422i	−0.267764	−	0.463781i
$34$		−	2.19615i		−	0.376637i
$35$		0			0
$36$	−0.366025	+	0.633975i	−0.0610042	+	0.105662i
$37$	4.12603	−	7.14650i	0.678316	−	1.17488i	−0.297172	−	0.954824i	$-0.596044\pi$
$37$	4.12603	−	7.14650i	0.678316	−	1.17488i	0.975488	−	0.220053i	$-0.0706231\pi$
$38$		−	8.35596i		−	1.35551i
$39$	2.29820	−	2.77818i	0.368006	−	0.444865i
$40$		0			0
$41$	2.87710	+	1.66109i	0.449327	+	0.259419i	0.707546	−	0.706667i	$-0.249802\pi$
$41$	2.87710	+	1.66109i	0.449327	+	0.259419i	−0.258219	+	0.966086i	$0.583136\pi$
$42$	2.78712	+	1.60915i	0.430063	+	0.248297i
$43$	−8.26772	+	4.77337i	−1.26082	+	0.727932i	−0.973232	−	0.229824i	$-0.926185\pi$
$43$	−8.26772	+	4.77337i	−1.26082	+	0.727932i	−0.287583	+	0.957756i	$0.592852\pi$
$44$		−	2.25207i		−	0.339512i
$45$		0			0
$46$	8.57425	−	4.95035i	1.26420	−	0.729889i
$47$	−1.79759			−0.262205			−0.131103	−	0.991369i	$-0.541852\pi$
$47$	−1.79759			−0.262205			−0.131103	+	0.991369i	$0.541852\pi$
$48$	1.73205	−	1.00000i	0.250000	−	0.144338i
$49$	−0.584320	+	1.01207i	−0.0834743	+	0.144582i
$50$		0			0
$51$	−1.95035			−0.273103
$52$	2.47388	−	0.920099i	0.343066	−	0.127595i
$53$			10.6569i			1.46384i	0.681393	+	0.731918i	$0.261375\pi$
$53$			10.6569i			1.46384i	−0.681393	+	0.731918i	$0.738625\pi$
$54$	−0.975173	−	0.563016i	−0.132704	−	0.0766168i
$55$		0			0
$56$	4.39627	+	7.61457i	0.587477	+	1.01754i
$57$	−7.42071			−0.982896
$58$	−3.76230	−	6.51649i	−0.494014	−	0.855657i
$59$	−4.17256	+	2.40903i	−0.543221	+	0.313629i	−0.746383	−	0.665516i	$-0.768211\pi$
$59$	−4.17256	+	2.40903i	−0.543221	+	0.313629i	0.203162	+	0.979145i	$0.434878\pi$
$60$		0			0
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	0.993879	−	0.110476i	$-0.0352375\pi$
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	−0.592614	+	0.805486i	$0.701904\pi$
$62$	3.07448	+	1.77505i	0.390460	+	0.225432i
$63$	1.42904	−	2.47517i	0.180042	−	0.311842i
$64$	8.39230			1.04904
$65$		0			0
$66$	3.46410			0.426401
$67$	−2.93927	+	5.09097i	−0.359090	+	0.621961i	−0.987809	−	0.155671i	$-0.950246\pi$
$67$	−2.93927	+	5.09097i	−0.359090	+	0.621961i	0.628719	+	0.777632i	$0.283579\pi$
$68$	−1.23647	−	0.713876i	−0.149944	−	0.0865702i
$69$	−4.39627	−	7.61457i	−0.529249	−	0.916686i
$70$		0			0
$71$	8.91942	−	5.14963i	1.05854	−	0.611148i	0.133512	−	0.991047i	$-0.457375\pi$
$71$	8.91942	−	5.14963i	1.05854	−	0.611148i	0.925028	+	0.379899i	$0.124041\pi$
$72$	−1.53819	−	2.66422i	−0.181277	−	0.313982i
$73$	11.1101			1.30034			0.650172	−	0.759787i	$-0.274697\pi$
$73$	11.1101			1.30034			0.650172	+	0.759787i	$0.274697\pi$
$74$	4.64605	+	8.04719i	0.540092	+	0.935467i
$75$		0			0
$76$	−4.70454	−	2.71617i	−0.539648	−	0.311566i
$77$			8.79254i			1.00200i
$78$	1.41529	+	3.80530i	0.160250	+	0.430865i
$79$	11.0968			1.24849			0.624246	−	0.781228i	$-0.285406\pi$
$79$	11.0968			1.24849			0.624246	+	0.781228i	$0.285406\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.23970	+	1.87044i	−0.357765	+	0.206556i
$83$	−6.97707			−0.765833			−0.382916	−	0.923783i	$-0.625080\pi$
$83$	−6.97707			−0.765833			−0.382916	+	0.923783i	$0.625080\pi$
$84$	1.81195	−	1.04613i	0.197700	−	0.114142i
$85$		0			0
$86$		−	10.7499i		−	1.15920i
$87$	−5.78712	+	3.34120i	−0.620445	+	0.358214i
$88$	8.19615	+	4.73205i	0.873713	+	0.504438i
$89$	−0.0805845	−	0.0465255i	−0.00854194	−	0.00493169i	0.495723	−	0.868481i	$-0.334903\pi$
$89$	−0.0805845	−	0.0465255i	−0.00854194	−	0.00493169i	−0.504265	+	0.863549i	$0.668236\pi$
$90$		0			0
$91$	−9.65857	+	3.59226i	−1.01249	+	0.376571i
$92$		−	6.43659i		−	0.671061i
$93$	1.57638	−	2.73037i	0.163463	−	0.283126i
$94$	1.01207	−	1.75296i	0.104387	−	0.180804i
$95$		0			0
$96$		−	3.90069i		−	0.398113i
$97$	−2.39879	−	4.15483i	−0.243561	−	0.421860i	0.718165	−	0.695873i	$-0.244982\pi$
$97$	−2.39879	−	4.15483i	−0.243561	−	0.421860i	−0.961726	+	0.274013i	$0.911649\pi$
$98$	−0.657963	−	1.13963i	−0.0664643	−	0.115120i
$99$		−	3.07638i		−	0.309188i
$100$		0			0
$101$	1.39627	−	2.41841i	0.138934	−	0.240641i	−0.788159	−	0.615471i	$-0.788966\pi$
$101$	1.39627	−	2.41841i	0.138934	−	0.240641i	0.927093	+	0.374830i	$0.122299\pi$
$102$	1.09808	−	1.90192i	0.108726	−	0.188319i
$103$		−	8.35395i		−	0.823139i	−0.911378	−	0.411570i	$-0.864981\pi$
$103$		−	8.35395i		−	0.823139i	0.911378	−	0.411570i	$-0.135019\pi$
$104$	−1.84953	+	10.9368i	−0.181362	+	1.07244i
$105$		0			0
$106$	−10.3923	−	6.00000i	−1.00939	−	0.582772i
$107$	5.49977	+	3.17529i	0.531683	+	0.306967i	0.741701	−	0.670730i	$-0.234019\pi$
$107$	5.49977	+	3.17529i	0.531683	+	0.306967i	−0.210019	+	0.977697i	$0.567352\pi$
$108$	−0.633975	+	0.366025i	−0.0610042	+	0.0352208i
$109$		−	11.7996i		−	1.13020i	−0.825024	−	0.565098i	$-0.808838\pi$
$109$		−	11.7996i		−	1.13020i	0.825024	−	0.565098i	$-0.191162\pi$
$110$		0			0
$111$	7.14650	−	4.12603i	0.678316	−	0.391626i
$112$	−5.71617			−0.540127
$113$	3.00000	−	1.73205i	0.282216	−	0.162938i	−0.352210	−	0.935921i	$-0.614570\pi$
$113$	3.00000	−	1.73205i	0.282216	−	0.162938i	0.634426	+	0.772983i	$0.281236\pi$
$114$	4.17798	−	7.23647i	0.391303	−	0.677757i
$115$		0			0
$116$	−4.89185			−0.454197
$117$	3.37939	−	1.25688i	0.312424	−	0.116198i
$118$		−	5.42529i		−	0.499438i
$119$	4.82744	+	2.78712i	0.442531	+	0.255495i
$120$		0			0
$121$	−0.767949	−	1.33013i	−0.0698136	−	0.120921i
$122$	−7.05791			−0.638994
$123$	1.66109	+	2.87710i	0.149776	+	0.259419i
$124$	1.99877	−	1.15399i	0.179495	−	0.103631i
$125$		0			0
$126$	1.60915	+	2.78712i	0.143354	+	0.248297i
$127$	12.9662	+	7.48601i	1.15056	+	0.664276i	0.949024	−	0.315205i	$-0.102073\pi$
$127$	12.9662	+	7.48601i	1.15056	+	0.664276i	0.201536	+	0.979481i	$0.435407\pi$
$128$	−0.824313	+	1.42775i	−0.0728597	+	0.126197i
$129$	−9.54674			−0.840543
$130$		0			0
$131$	−10.5831			−0.924649			−0.462324	−	0.886711i	$-0.652984\pi$
$131$	−10.5831			−0.924649			−0.462324	+	0.886711i	$0.652984\pi$
$132$	1.12603	−	1.95035i	0.0980085	−	0.169756i
$133$	18.3675	+	10.6045i	1.59267	+	0.919526i
$134$	−3.30972	−	5.73260i	−0.285916	−	0.495221i
$135$		0			0
$136$	5.19615	−	3.00000i	0.445566	−	0.257248i
$137$	−4.35327	−	7.54009i	−0.371925	−	0.644193i	0.617937	−	0.786228i	$-0.287969\pi$
$137$	−4.35327	−	7.54009i	−0.371925	−	0.644193i	−0.989862	+	0.142035i	$0.954635\pi$
$138$	9.90069			0.842803
$139$	−5.82844	−	10.0952i	−0.494362	−	0.856260i	0.505617	−	0.862758i	$-0.331265\pi$
$139$	−5.82844	−	10.0952i	−0.494362	−	0.856260i	−0.999979	+	0.00649792i	$0.997932\pi$
$140$		0			0
$141$	−1.55676	−	0.898795i	−0.131103	−	0.0756922i
$142$			11.5973i			0.973223i
$143$	−7.07012	+	8.54674i	−0.591233	+	0.714714i
$144$	2.00000			0.166667
$145$		0			0
$146$	−6.25519	+	10.8343i	−0.517684	+	0.896654i
$147$	−1.01207	+	0.584320i	−0.0834743	+	0.0481939i
$148$	6.04093			0.496561
$149$	−5.91003	+	3.41216i	−0.484168	+	0.279535i	−0.722152	−	0.691734i	$-0.756847\pi$
$149$	−5.91003	+	3.41216i	−0.484168	+	0.279535i	0.237984	+	0.971269i	$0.423514\pi$
$150$		0			0
$151$			12.6810i			1.03197i	0.856598	+	0.515984i	$0.172574\pi$
$151$			12.6810i			1.03197i	−0.856598	+	0.515984i	$0.827426\pi$
$152$	19.7704	−	11.4144i	1.60359	−	0.925834i
$153$	−1.68905	−	0.975173i	−0.136551	−	0.0788380i
$154$	−8.57425	−	4.95035i	−0.690933	−	0.398910i
$155$		0			0
$156$	2.60249	+	0.440113i	0.208366	+	0.0352372i
$157$		−	7.98333i		−	0.637139i	−0.947900	−	0.318569i	$-0.896798\pi$
$157$		−	7.98333i		−	0.637139i	0.947900	−	0.318569i	$-0.103202\pi$
$158$	−6.24770	+	10.8213i	−0.497041	+	0.860900i
$159$	−5.32844	+	9.22913i	−0.422573	+	0.731918i
$160$		0			0
$161$			25.1298i			1.98051i
$162$	−0.563016	−	0.975173i	−0.0442347	−	0.0766168i
$163$	−6.16109	−	10.6713i	−0.482574	−	0.835843i	0.517226	−	0.855849i	$-0.326965\pi$
$163$	−6.16109	−	10.6713i	−0.482574	−	0.835843i	−0.999800	+	0.0200063i	$0.993631\pi$
$164$			2.43201i			0.189908i
$165$		0			0
$166$	3.92820	−	6.80385i	0.304888	−	0.528081i
$167$	−10.9708	+	19.0020i	−0.848947	+	1.47042i	0.0332022	+	0.999449i	$0.489429\pi$
$167$	−10.9708	+	19.0020i	−0.848947	+	1.47042i	−0.882149	+	0.470970i	$0.843904\pi$
$168$			8.79254i			0.678360i
$169$	−12.2771	−	4.27466i	−0.944393	−	0.328820i
$170$		0			0
$171$	−6.42652	−	3.71035i	−0.491448	−	0.283738i
$172$	−6.05239	−	3.49435i	−0.461490	−	0.266442i
$173$	−13.0342	+	7.52528i	−0.990969	+	0.572136i	−0.905564	−	0.424210i	$-0.860552\pi$
$173$	−13.0342	+	7.52528i	−0.990969	+	0.572136i	−0.0854053	+	0.996346i	$0.527219\pi$
$174$		−	7.52460i		−	0.570438i
$175$		0			0
$176$	−5.32844	+	3.07638i	−0.401647	+	0.231891i
$177$	−4.81805			−0.362147
$178$	0.0907407	−	0.0523892i	0.00680130	−	0.00392673i
$179$	0.240387	−	0.416363i	0.0179674	−	0.0311204i	−0.856902	−	0.515480i	$-0.827614\pi$
$179$	0.240387	−	0.416363i	0.0179674	−	0.0311204i	0.874869	+	0.484359i	$0.160947\pi$
$180$		0			0
$181$	−1.85887			−0.138169			−0.0690844	−	0.997611i	$-0.522008\pi$
$181$	−1.85887			−0.138169			−0.0690844	+	0.997611i	$0.522008\pi$
$182$	1.93486	−	11.4413i	0.143421	−	0.848084i
$183$			6.26795i			0.463340i
$184$	23.4253	+	13.5246i	1.72694	+	0.997046i
$185$		0			0
$186$	1.77505	+	3.07448i	0.130153	+	0.225432i
$187$	6.00000			0.438763
$188$	−0.657963	−	1.13963i	−0.0479869	−	0.0831158i
$189$	2.47517	−	1.42904i	0.180042	−	0.103947i
$190$		0			0
$191$	−4.35937	−	7.55066i	−0.315433	−	0.546346i	0.664096	−	0.747647i	$-0.268816\pi$
$191$	−4.35937	−	7.55066i	−0.315433	−	0.546346i	−0.979529	+	0.201301i	$0.935483\pi$
$192$	7.26795	+	4.19615i	0.524519	+	0.302831i
$193$	−3.22663	+	5.58869i	−0.232258	+	0.402283i	−0.958472	−	0.285186i	$-0.907945\pi$
$193$	−3.22663	+	5.58869i	−0.232258	+	0.402283i	0.726214	+	0.687468i	$0.241278\pi$
$194$	5.40224			0.387858
$195$		0			0
$196$	−0.855504			−0.0611074
$197$	5.79651	−	10.0399i	0.412984	−	0.715310i	−0.582230	−	0.813024i	$-0.697820\pi$
$197$	5.79651	−	10.0399i	0.412984	−	0.715310i	0.995215	+	0.0977141i	$0.0311531\pi$
$198$	3.00000	+	1.73205i	0.213201	+	0.123091i
$199$	−0.400691	−	0.694017i	−0.0284042	−	0.0491976i	0.851474	−	0.524397i	$-0.175709\pi$
$199$	−0.400691	−	0.694017i	−0.0284042	−	0.0491976i	−0.879878	+	0.475199i	$0.842376\pi$
$200$		0			0
$201$	−5.09097	+	2.93927i	−0.359090	+	0.207320i
$202$	1.57225	+	2.72321i	0.110623	+	0.191605i
$203$	19.0988			1.34048
$204$	−0.713876	−	1.23647i	−0.0499813	−	0.0865702i
$205$		0			0
$206$	8.14655	+	4.70341i	0.567597	+	0.327702i
$207$		−	8.79254i		−	0.611124i
$208$	−5.55636	−	4.59639i	−0.385265	−	0.318702i
$209$	22.8289			1.57911
$210$		0			0
$211$	4.14605	−	7.18116i	0.285426	−	0.494372i	−0.687287	−	0.726386i	$-0.741198\pi$
$211$	4.14605	−	7.18116i	0.285426	−	0.494372i	0.972712	+	0.232015i	$0.0745317\pi$
$212$	−6.75620	+	3.90069i	−0.464017	+	0.267901i
$213$	10.2993			0.705693
$214$	−6.19292	+	3.57548i	−0.423339	+	0.244415i
$215$		0			0
$216$		−	3.07638i		−	0.209321i
$217$	−7.80362	+	4.50542i	−0.529744	+	0.305848i
$218$	11.5066	+	6.64336i	0.779328	+	0.449945i
$219$	9.62167	+	5.55507i	0.650172	+	0.375377i
$220$		0			0
$221$	2.45135	+	6.59097i	0.164895	+	0.443357i
$222$			9.29209i			0.623644i
$223$	−6.38068	+	11.0517i	−0.427282	+	0.740074i	−0.996630	−	0.0820224i	$-0.973862\pi$
$223$	−6.38068	+	11.0517i	−0.427282	+	0.740074i	0.569349	+	0.822096i	$0.307195\pi$
$224$	−5.57425	+	9.65488i	−0.372445	+	0.645094i
$225$		0			0
$226$			3.90069i			0.259470i
$227$	8.55568	+	14.8189i	0.567860	+	0.983563i	0.996777	+	0.0802192i	$0.0255620\pi$
$227$	8.55568	+	14.8189i	0.567860	+	0.983563i	−0.428917	+	0.903344i	$0.641105\pi$
$228$	−2.71617	−	4.70454i	−0.179883	−	0.311566i
$229$		−	6.39993i		−	0.422919i	−0.977387	−	0.211460i	$-0.932178\pi$
$229$		−	6.39993i		−	0.422919i	0.977387	−	0.211460i	$-0.0678217\pi$
$230$		0			0
$231$	−4.39627	+	7.61457i	−0.289253	+	0.501002i
$232$	10.2788	−	17.8034i	0.674836	−	1.16885i
$233$		−	0.671557i		−	0.0439952i	−0.999758	−	0.0219976i	$-0.992997\pi$
$233$		−	0.671557i		−	0.0439952i	0.999758	−	0.0219976i	$-0.00700261\pi$
$234$	−0.676977	+	4.00313i	−0.0442553	+	0.261693i
$235$		0			0
$236$	−3.05452	−	1.76353i	−0.198833	−	0.114796i
$237$	9.61015	+	5.54842i	0.624246	+	0.360409i
$238$	−5.43586	+	3.13839i	−0.352354	+	0.203432i
$239$		−	7.12983i		−	0.461190i	−0.973050	−	0.230595i	$-0.925933\pi$
$239$		−	7.12983i		−	0.461190i	0.973050	−	0.230595i	$-0.0740673\pi$
$240$		0			0
$241$	−23.3292	+	13.4691i	−1.50277	+	0.867623i	−0.502772	+	0.864419i	$0.667686\pi$
$241$	−23.3292	+	13.4691i	−1.50277	+	0.867623i	−0.999995	+	0.00320355i	$0.998980\pi$
$242$	1.72947			0.111175
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.29423	+	3.97372i	−0.146873	+	0.254391i
$245$		0			0
$246$	−3.74089			−0.238510
$247$	9.32692	+	25.0774i	0.593458	+	1.59564i
$248$			9.69907i			0.615892i
$249$	−6.04232	−	3.48853i	−0.382916	−	0.221077i
$250$		0			0
$251$	−5.82402	−	10.0875i	−0.367609	−	0.636718i	0.621582	−	0.783349i	$-0.286490\pi$
$251$	−5.82402	−	10.0875i	−0.367609	−	0.636718i	−0.989191	+	0.146631i	$0.953157\pi$
$252$	2.09226			0.131800
$253$	13.5246	+	23.4253i	0.850284	+	1.47274i
$254$	−14.6003	+	8.42949i	−0.916105	+	0.528913i
$255$		0			0
$256$	7.46410	+	12.9282i	0.466506	+	0.808013i
$257$	6.30362	+	3.63939i	0.393209	+	0.227019i	0.683550	−	0.729904i	$-0.260435\pi$
$257$	6.30362	+	3.63939i	0.393209	+	0.227019i	−0.290341	+	0.956923i	$0.593769\pi$
$258$	5.37497	−	9.30972i	0.334631	−	0.579598i
$259$	−23.5851			−1.46551
$260$		0			0
$261$	−6.68240			−0.413630
$262$	5.95845	−	10.3203i	0.368114	−	0.637593i
$263$	−20.7220	−	11.9639i	−1.27778	−	0.737724i	−0.301336	−	0.953518i	$-0.597433\pi$
$263$	−20.7220	−	11.9639i	−1.27778	−	0.737724i	−0.976439	+	0.215794i	$0.930766\pi$
$264$	4.73205	+	8.19615i	0.291238	+	0.504438i
$265$		0			0
$266$	−20.6824	+	11.9410i	−1.26812	+	0.732150i
$267$	−0.0465255	−	0.0805845i	−0.00284731	−	0.00493169i
$268$	−4.30340			−0.262872
$269$	2.19073	+	3.79446i	0.133571	+	0.231352i	0.925051	−	0.379843i	$-0.124022\pi$
$269$	2.19073	+	3.79446i	0.133571	+	0.231352i	−0.791479	+	0.611196i	$0.790689\pi$
$270$		0			0
$271$	−2.15488	−	1.24412i	−0.130900	−	0.0755751i	0.433120	−	0.901336i	$-0.357413\pi$
$271$	−2.15488	−	1.24412i	−0.130900	−	0.0755751i	−0.564020	+	0.825761i	$0.690746\pi$
$272$			3.90069i			0.236514i
$273$	−10.1607	−	1.71829i	−0.614953	−	0.103996i
$274$	9.80385			0.592272
$275$		0			0
$276$	3.21829	−	5.57425i	0.193719	−	0.335530i
$277$	−18.7980	+	10.8530i	−1.12946	+	0.652096i	−0.943800	−	0.330518i	$-0.892777\pi$
$277$	−18.7980	+	10.8530i	−1.12946	+	0.652096i	−0.185663	+	0.982613i	$0.559443\pi$
$278$	13.1260			0.787247
$279$	2.73037	−	1.57638i	0.163463	−	0.0943753i
$280$		0			0
$281$		−	29.7270i		−	1.77336i	−0.462379	−	0.886682i	$-0.653004\pi$
$281$		−	29.7270i		−	1.77336i	0.462379	−	0.886682i	$-0.346996\pi$
$282$	1.75296	−	1.01207i	0.104387	−	0.0602680i
$283$	24.2483	+	13.9998i	1.44141	+	0.832200i	0.997944	−	0.0640902i	$-0.0204145\pi$
$283$	24.2483	+	13.9998i	1.44141	+	0.832200i	0.443468	+	0.896290i	$0.353748\pi$
$284$	6.52947	+	3.76979i	0.387452	+	0.223696i
$285$		0			0
$286$	−4.35395	−	11.7065i	−0.257455	−	0.692222i
$287$		−	9.49508i		−	0.560477i
$288$	1.95035	−	3.37810i	0.114925	−	0.199056i
$289$	−6.59808	+	11.4282i	−0.388122	+	0.672247i
$290$		0			0
$291$		−	4.79759i		−	0.281240i
$292$	4.06660	+	7.04355i	0.237980	+	0.412193i
$293$	−8.47930	−	14.6866i	−0.495366	−	0.857999i	0.504620	−	0.863342i	$-0.331633\pi$
$293$	−8.47930	−	14.6866i	−0.495366	−	0.857999i	−0.999986	+	0.00534246i	$0.998299\pi$
$294$		−	1.31593i		−	0.0767464i
$295$		0			0
$296$	−12.6932	+	21.9853i	−0.737779	+	1.27787i
$297$	1.53819	−	2.66422i	0.0892548	−	0.154594i
$298$		−	7.68440i		−	0.445145i
$299$	−20.2070	+	24.4273i	−1.16860	+	1.41267i
$300$		0			0
$301$	23.6298	+	13.6427i	1.36200	+	0.786351i
$302$	−12.3662	−	7.13963i	−0.711595	−	0.410839i
$303$	2.41841	−	1.39627i	0.138934	−	0.0802137i
$304$			14.8414i			0.851213i
$305$		0			0
$306$	1.90192	−	1.09808i	0.108726	−	0.0627728i
$307$	−15.6072			−0.890752			−0.445376	−	0.895344i	$-0.646930\pi$
$307$	−15.6072			−0.890752			−0.445376	+	0.895344i	$0.646930\pi$
$308$	−5.57425	+	3.21829i	−0.317622	+	0.183379i
$309$	4.17698	−	7.23474i	0.237620	−	0.411570i
$310$		0			0
$311$	24.9941			1.41728			0.708642	−	0.705568i	$-0.249308\pi$
$311$	24.9941			1.41728			0.708642	+	0.705568i	$0.249308\pi$
$312$	−7.07012	+	8.54674i	−0.400267	+	0.483864i
$313$			1.16117i			0.0656331i	0.999461	+	0.0328166i	$0.0104477\pi$
$313$			1.16117i			0.0656331i	−0.999461	+	0.0328166i	$0.989552\pi$
$314$	7.78512	+	4.49474i	0.439340	+	0.253653i
$315$		0			0
$316$	4.06173	+	7.03512i	0.228490	+	0.395756i
$317$	8.62570			0.484467			0.242234	−	0.970218i	$-0.422120\pi$
$317$	8.62570			0.484467			0.242234	+	0.970218i	$0.422120\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$	17.8034	−	10.2788i	0.996798	−	0.575502i
$320$		0			0
$321$	3.17529	+	5.49977i	0.177228	+	0.306967i
$322$	−24.5059	−	14.1485i	−1.36566	−	0.788465i
$323$	7.23647	−	12.5339i	0.402648	−	0.697407i
$324$	−0.732051			−0.0406695
$325$		0			0
$326$	13.8752			0.768475
$327$	5.89980	−	10.2187i	0.326259	−	0.565098i
$328$	−8.85104	−	5.11015i	−0.488717	−	0.282161i
$329$	2.56883	+	4.44934i	0.141624	+	0.245300i
$330$		0			0
$331$	−22.1899	+	12.8113i	−1.21967	+	0.704174i	−0.964846	−	0.262815i	$-0.915349\pi$
$331$	−22.1899	+	12.8113i	−1.21967	+	0.704174i	−0.254819	+	0.966989i	$0.582016\pi$
$332$	−2.55378	−	4.42328i	−0.140157	−	0.242759i
$333$	8.25207			0.452210
$334$	−12.3535	−	21.3969i	−0.675953	−	1.17078i
$335$		0			0
$336$	−4.95035	−	2.85808i	−0.270063	−	0.155921i
$337$			20.1770i			1.09911i	0.835457	+	0.549556i	$0.185203\pi$
$337$			20.1770i			1.09911i	−0.835457	+	0.549556i	$0.814797\pi$
$338$	11.0807	−	9.56560i	0.602713	−	0.520300i
$339$	3.46410			0.188144
$340$		0			0
$341$	−4.84953	+	8.39964i	−0.262617	+	0.454866i
$342$	7.23647	−	4.17798i	0.391303	−	0.225919i
$343$	−16.6665			−0.899907
$344$	25.4346	−	14.6847i	1.37134	−	0.791745i
$345$		0			0
$346$		−	16.9474i		−	0.911099i
$347$	−20.9523	+	12.0968i	−1.12478	+	0.649393i	−0.942617	−	0.333876i	$-0.891643\pi$
$347$	−20.9523	+	12.0968i	−1.12478	+	0.649393i	−0.182164	+	0.983268i	$0.558310\pi$
$348$	−4.23647	−	2.44593i	−0.227099	−	0.131115i
$349$	−22.2362	−	12.8381i	−1.19028	−	0.687206i	−0.231907	−	0.972738i	$-0.574496\pi$
$349$	−22.2362	−	12.8381i	−1.19028	−	0.687206i	−0.958369	+	0.285532i	$0.907830\pi$
$350$		0			0
$351$	3.55507	+	0.601205i	0.189756	+	0.0320900i
$352$			12.0000i			0.639602i
$353$	3.92254	−	6.79405i	0.208776	−	0.361611i	−0.742553	−	0.669787i	$-0.766385\pi$
$353$	3.92254	−	6.79405i	0.208776	−	0.361611i	0.951329	+	0.308176i	$0.0997187\pi$
$354$	2.71264	−	4.69844i	0.144175	−	0.249719i
$355$		0			0
$356$		−	0.0681180i		−	0.00361025i
$357$	2.78712	+	4.82744i	0.147510	+	0.255495i
$358$	0.270684	+	0.468838i	0.0143061	+	0.0247789i
$359$		−	19.7145i		−	1.04049i	−0.854017	−	0.520245i	$-0.825840\pi$
$359$		−	19.7145i		−	1.04049i	0.854017	−	0.520245i	$-0.174160\pi$
$360$		0			0
$361$	18.0334	−	31.2348i	0.949128	−	1.64394i
$362$	1.04658	−	1.81272i	0.0550068	−	0.0952745i
$363$		−	1.53590i		−	0.0806138i
$364$	−5.81268	−	4.80843i	−0.304667	−	0.252030i
$365$		0			0
$366$	−6.11233	−	3.52896i	−0.319497	−	0.184462i
$367$	−9.67880	−	5.58806i	−0.505229	−	0.291694i	0.225641	−	0.974210i	$-0.427552\pi$
$367$	−9.67880	−	5.58806i	−0.505229	−	0.291694i	−0.730870	+	0.682516i	$0.760886\pi$
$368$	−15.2291	+	8.79254i	−0.793873	+	0.458343i
$369$			3.32218i			0.172946i
$370$		0			0
$371$	26.3776	−	15.2291i	1.36946	−	0.790657i
$372$	2.30798			0.119663
$373$	−7.57922	+	4.37586i	−0.392437	+	0.226574i	−0.683216	−	0.730217i	$-0.739419\pi$
$373$	−7.57922	+	4.37586i	−0.392437	+	0.226574i	0.290778	+	0.956790i	$0.406086\pi$
$374$	−3.37810	+	5.85104i	−0.174677	+	0.302550i
$375$		0			0
$376$	5.53006			0.285191
$377$	18.5649	+	15.3575i	0.956142	+	0.790949i
$378$			3.21829i			0.165531i
$379$	16.2550	+	9.38481i	0.834961	+	0.482065i	0.855548	−	0.517723i	$-0.173220\pi$
$379$	16.2550	+	9.38481i	0.834961	+	0.482065i	−0.0205870	+	0.999788i	$0.506554\pi$
$380$		0			0
$381$	7.48601	+	12.9662i	0.383520	+	0.664276i
$382$	9.81759			0.502312
$383$	3.03734	+	5.26083i	0.155201	+	0.268816i	0.933132	−	0.359533i	$-0.117064\pi$
$383$	3.03734	+	5.26083i	0.155201	+	0.268816i	−0.777931	+	0.628349i	$0.783731\pi$
$384$	−1.42775	+	0.824313i	−0.0728597	+	0.0420655i
$385$		0			0
$386$	−3.63329	−	6.29305i	−0.184930	−	0.320308i
$387$	−8.26772	−	4.77337i	−0.420272	−	0.242644i
$388$	1.75604	−	3.04155i	0.0891494	−	0.154411i
$389$	−9.66572			−0.490072			−0.245036	−	0.969514i	$-0.578800\pi$
$389$	−9.66572			−0.490072			−0.245036	+	0.969514i	$0.578800\pi$
$390$		0			0
$391$	17.1485			0.867237
$392$	1.79759	−	3.11352i	0.0907920	−	0.157256i
$393$	−9.16522	−	5.29154i	−0.462324	−	0.266923i
$394$	6.52706	+	11.3052i	0.328829	+	0.569548i
$395$		0			0
$396$	1.95035	−	1.12603i	0.0980085	−	0.0565853i
$397$	−12.1658	−	21.0718i	−0.610585	−	1.05757i	−0.991142	−	0.132807i	$-0.957601\pi$
$397$	−12.1658	−	21.0718i	−0.610585	−	1.05757i	0.380556	−	0.924758i	$-0.375732\pi$
$398$	0.902382			0.0452323
$399$	10.6045	+	18.3675i	0.530889	+	0.919526i
$400$		0			0
$401$	−7.70454	−	4.44822i	−0.384746	−	0.222133i	0.295135	−	0.955456i	$-0.404635\pi$
$401$	−7.70454	−	4.44822i	−0.384746	−	0.222133i	−0.679881	+	0.733322i	$0.737969\pi$
$402$		−	6.61944i		−	0.330148i
$403$	−11.2083	−	1.89545i	−0.558324	−	0.0944193i
$404$	2.04428			0.101707
$405$		0			0
$406$	−10.7530	+	18.6247i	−0.533660	+	0.924327i
$407$	−21.9853	+	12.6932i	−1.08977	+	0.629180i
$408$	6.00000			0.297044
$409$	−24.4988	+	14.1444i	−1.21139	+	0.699394i	−0.963061	−	0.269283i	$-0.913213\pi$
$409$	−24.4988	+	14.1444i	−1.21139	+	0.699394i	−0.248325	+	0.968677i	$0.579880\pi$
$410$		0			0
$411$		−	8.70654i		−	0.429462i
$412$	5.29619	−	3.05776i	0.260925	−	0.150645i
$413$	11.9255	+	6.88520i	0.586816	+	0.338799i
$414$	8.57425	+	4.95035i	0.421401	+	0.243296i
$415$		0			0
$416$	−13.1819	+	4.90269i	−0.646298	+	0.240374i
$417$		−	11.6569i		−	0.570840i
$418$	−12.8530	+	22.2621i	−0.628663	+	1.08888i
$419$	14.4474	−	25.0236i	0.705801	−	1.22248i	−0.260601	−	0.965447i	$-0.583921\pi$
$419$	14.4474	−	25.0236i	0.705801	−	1.22248i	0.966402	−	0.257036i	$-0.0827459\pi$
$420$		0			0
$421$			12.0134i			0.585498i	0.956189	+	0.292749i	$0.0945701\pi$
$421$			12.0134i			0.585498i	−0.956189	+	0.292749i	$0.905430\pi$
$422$	4.66858	+	8.08622i	0.227263	+	0.393631i
$423$	−0.898795	−	1.55676i	−0.0437009	−	0.0756922i
$424$		−	32.7846i		−	1.59216i
$425$		0			0
$426$	−5.79865	+	10.0436i	−0.280945	+	0.486612i
$427$	8.95716	−	15.5143i	0.433467	−	0.750788i
$428$			4.64895i			0.224716i
$429$	−10.3963	+	3.86663i	−0.501937	+	0.186683i
$430$		0			0
$431$	19.9384	+	11.5115i	0.960401	+	0.554488i	0.896296	−	0.443455i	$-0.146248\pi$
$431$	19.9384	+	11.5115i	0.960401	+	0.554488i	0.0641046	+	0.997943i	$0.479581\pi$
$432$	1.73205	+	1.00000i	0.0833333	+	0.0481125i
$433$	23.2783	−	13.4397i	1.11868	−	0.645872i	0.177619	−	0.984099i	$-0.443161\pi$
$433$	23.2783	−	13.4397i	1.11868	−	0.645872i	0.941064	+	0.338227i	$0.109827\pi$
$434$		−	10.1465i		−	0.487047i
$435$		0			0
$436$	7.48064	−	4.31895i	0.358258	−	0.206840i
$437$	65.2469			3.12118
$438$	−10.8343	+	6.25519i	−0.517684	+	0.298885i
$439$	15.8272	−	27.4135i	0.755392	−	1.30838i	−0.189788	−	0.981825i	$-0.560780\pi$
$439$	15.8272	−	27.4135i	0.755392	−	1.30838i	0.945179	−	0.326551i	$-0.105887\pi$
$440$		0			0
$441$	−1.16864			−0.0556495
$442$	−7.80748	−	1.32034i	−0.371364	−	0.0628021i
$443$		−	9.89932i		−	0.470331i	−0.971955	−	0.235166i	$-0.924437\pi$
$443$		−	9.89932i		−	0.470331i	0.971955	−	0.235166i	$-0.0755632\pi$
$444$	5.23160	+	3.02047i	0.248281	+	0.143345i
$445$		0			0
$446$	−7.18485	−	12.4445i	−0.340212	−	0.589265i
$447$	−6.82431			−0.322779
$448$	−11.9930	−	20.7724i	−0.566614	−	0.981404i
$449$	12.9975	−	7.50413i	0.613392	−	0.354142i	−0.160900	−	0.986971i	$-0.551440\pi$
$449$	12.9975	−	7.50413i	0.613392	−	0.354142i	0.774292	+	0.632829i	$0.218106\pi$
$450$		0			0
$451$	−5.11015	−	8.85104i	−0.240627	−	0.416779i
$452$	2.19615	+	1.26795i	0.103298	+	0.0596393i
$453$	−6.34052	+	10.9821i	−0.297903	+	0.515984i
$454$	−19.2679			−0.904290
$455$		0			0
$456$	22.8289			1.06906
$457$	−6.51520	+	11.2847i	−0.304768	+	0.527874i	−0.977210	−	0.212276i	$-0.931912\pi$
$457$	−6.51520	+	11.2847i	−0.304768	+	0.527874i	0.672441	+	0.740150i	$0.265246\pi$
$458$	6.24104	+	3.60326i	0.291624	+	0.168369i
$459$	−0.975173	−	1.68905i	−0.0455172	−	0.0788380i
$460$		0			0
$461$	24.8693	−	14.3583i	1.15828	−	0.668732i	0.207388	−	0.978259i	$-0.433504\pi$
$461$	24.8693	−	14.3583i	1.15828	−	0.668732i	0.950891	+	0.309526i	$0.100170\pi$
$462$	−4.95035	−	8.57425i	−0.230311	−	0.398910i
$463$	0.460309			0.0213924			0.0106962	−	0.999943i	$-0.496595\pi$
$463$	0.460309			0.0213924			0.0106962	+	0.999943i	$0.496595\pi$
$464$	6.68240	+	11.5742i	0.310222	+	0.537321i
$465$		0			0
$466$	0.654884	+	0.378098i	0.0303369	+	0.0175150i
$467$		−	34.0634i		−	1.57627i	−0.615505	−	0.788133i	$-0.711048\pi$
$467$		−	34.0634i		−	1.57627i	0.615505	−	0.788133i	$-0.288952\pi$
$468$	2.03377	+	1.68240i	0.0940111	+	0.0777688i
$469$	16.8014			0.775816
$470$		0			0
$471$	3.99166	−	6.91376i	0.183926	−	0.318569i
$472$	12.8364	−	7.41108i	0.590842	−	0.341123i
$473$	29.3694			1.35041
$474$	−10.8213	+	6.24770i	−0.497041	+	0.286967i
$475$		0			0
$476$			4.08063i			0.187036i
$477$	−9.22913	+	5.32844i	−0.422573	+	0.243973i
$478$	6.95281	+	4.01421i	0.318014	+	0.183606i
$479$	−26.7871	−	15.4656i	−1.22393	−	0.706639i	−0.258180	−	0.966097i	$-0.583123\pi$
$479$	−26.7871	−	15.4656i	−1.22393	−	0.706639i	−0.965755	+	0.259458i	$0.916456\pi$
$480$		0			0
$481$	−22.9257	−	18.9649i	−1.04532	−	0.864723i
$482$		−	30.3333i		−	1.38165i
$483$	−12.5649	+	21.7631i	−0.571723	+	0.990254i
$484$	0.562178	−	0.973721i	0.0255535	−	0.0442600i
$485$		0			0
$486$		−	1.12603i		−	0.0510779i
$487$	−8.26901	−	14.3223i	−0.374704	−	0.649007i	0.615578	−	0.788076i	$-0.288922\pi$
$487$	−8.26901	−	14.3223i	−0.374704	−	0.649007i	−0.990283	+	0.139069i	$0.955589\pi$
$488$	−9.64129	−	16.6992i	−0.436441	−	0.755937i
$489$		−	12.3222i		−	0.557228i
$490$		0			0
$491$	9.34120	−	16.1794i	0.421562	−	0.730167i	−0.574530	−	0.818483i	$-0.694815\pi$
$491$	9.34120	−	16.1794i	0.421562	−	0.730167i	0.996093	+	0.0883160i	$0.0281485\pi$
$492$	−1.21600	+	2.10618i	−0.0548217	+	0.0949540i
$493$		−	13.0330i		−	0.586976i
$494$	−29.7060	−	5.02364i	−1.33654	−	0.226024i
$495$		0			0
$496$	−5.46073	−	3.15276i	−0.245194	−	0.141563i
$497$	−25.4924	−	14.7181i	−1.14349	−	0.660195i
$498$	6.80385	−	3.92820i	0.304888	−	0.176027i
$499$		−	10.9966i		−	0.492277i	−0.969235	−	0.246138i	$-0.920838\pi$
$499$		−	10.9966i		−	0.492277i	0.969235	−	0.246138i	$-0.0791618\pi$
$500$		0			0
$501$	−19.0020	+	10.9708i	−0.848947	+	0.490140i
$502$	13.1161			0.585399
$503$	−13.8506	+	7.99663i	−0.617567	+	0.356552i	−0.775921	−	0.630830i	$-0.782714\pi$
$503$	−13.8506	+	7.99663i	−0.617567	+	0.356552i	0.158354	+	0.987382i	$0.449381\pi$
$504$	−4.39627	+	7.61457i	−0.195826	+	0.339180i
$505$		0			0
$506$	−30.4583			−1.35404
$507$	−8.49496	−	9.84052i	−0.377274	−	0.437033i
$508$			10.9603i			0.486284i
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	0.472347	−	0.881413i	$-0.343407\pi$
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	−0.527152	+	0.849771i	$0.676740\pi$
$510$		0			0
$511$	−15.8769	−	27.4995i	−0.702351	−	1.21651i
$512$	−20.1069			−0.888608
$513$	−3.71035	−	6.42652i	−0.163816	−	0.283738i
$514$	−7.09808	+	4.09808i	−0.313083	+	0.180758i
$515$		0			0
$516$	−3.49435	−	6.05239i	−0.153830	−	0.266442i
$517$	4.78918	+	2.76503i	0.210628	+	0.121606i
$518$	13.2788	−	22.9995i	0.583436	−	1.01054i
$519$	−15.0506			−0.660646
$520$		0			0
$521$	11.8172			0.517719			0.258859	−	0.965915i	$-0.416653\pi$
$521$	11.8172			0.517719			0.258859	+	0.965915i	$0.416653\pi$
$522$	3.76230	−	6.51649i	0.164671	−	0.285219i
$523$	−24.7792	−	14.3063i	−1.08352	−	0.625571i	−0.151677	−	0.988430i	$-0.548467\pi$
$523$	−24.7792	−	14.3063i	−1.08352	−	0.625571i	−0.931844	+	0.362859i	$0.881801\pi$
$524$	−3.87368	−	6.70941i	−0.169222	−	0.293102i
$525$		0			0
$526$	23.3337	−	13.4717i	1.01740	−	0.587394i
$527$	3.07448	+	5.32516i	0.133927	+	0.231968i
$528$	−6.15276			−0.267764
$529$	27.1544	+	47.0328i	1.18063	+	2.04491i
$530$		0			0
$531$	−4.17256	−	2.40903i	−0.181074	−	0.104543i
$532$			15.5261i			0.673140i
$533$	7.63503	−	9.22963i	0.330710	−	0.399780i
$534$	0.104778			0.00453420
$535$		0			0
$536$	9.04232	−	15.6618i	0.390569	−	0.676485i
$537$	0.416363	−	0.240387i	0.0179674	−	0.0103735i
$538$	−4.93367			−0.212706
$539$	3.11352	−	1.79759i	0.134109	−	0.0774277i
$540$		0			0
$541$			33.9315i			1.45883i	0.684072	+	0.729415i	$0.260208\pi$
$541$			33.9315i			1.45883i	−0.684072	+	0.729415i	$0.739792\pi$
$542$	2.42647	−	1.40092i	0.104226	−	0.0601748i
$543$	−1.60983	−	0.929436i	−0.0690844	−	0.0398859i
$544$	6.58846	+	3.80385i	0.282478	+	0.163089i
$545$		0			0
$546$	7.39627	−	8.94101i	0.316531	−	0.382640i
$547$			0.0276116i			0.00118059i	1.00000		0.000590294i	$0.000187896\pi$
$547$			0.0276116i			0.00118059i	−1.00000		0.000590294i	$0.999812\pi$
$548$	3.18682	−	5.51973i	0.136134	−	0.235791i
$549$	−3.13397	+	5.42820i	−0.133755	+	0.231670i
$550$		0			0
$551$		−	49.5881i		−	2.11252i
$552$	13.5246	+	23.4253i	0.575645	+	0.997046i
$553$	−15.8579	−	27.4666i	−0.674344	−	1.16800i
$554$		−	24.4417i		−	1.03843i
$555$		0			0
$556$	4.26672	−	7.39017i	0.180949	−	0.313413i
$557$	−20.1826	+	34.9572i	−0.855162	+	1.48118i	0.0213318	+	0.999772i	$0.493209\pi$
$557$	−20.1826	+	34.9572i	−0.855162	+	1.48118i	−0.876494	+	0.481412i	$0.840124\pi$
$558$			3.55011i			0.150288i
$559$	11.9991	+	32.2621i	0.507507	+	1.36454i
$560$		0			0
$561$	5.19615	+	3.00000i	0.219382	+	0.126660i
$562$	28.9890	+	16.7368i	1.22283	+	0.705999i
$563$	−12.2291	+	7.06049i	−0.515397	+	0.297564i	−0.735049	−	0.678014i	$-0.762841\pi$
$563$	−12.2291	+	7.06049i	−0.515397	+	0.297564i	0.219653	+	0.975578i	$0.429508\pi$
$564$		−	1.31593i		−	0.0554105i
$565$		0			0
$566$	−27.3044	+	15.7642i	−1.14769	+	0.662618i
$567$	2.85808			0.120028
$568$	−27.4395	+	15.8422i	−1.15134	+	0.664724i
$569$	15.5158	−	26.8742i	0.650456	−	1.12662i	−0.332556	−	0.943084i	$-0.607911\pi$
$569$	15.5158	−	26.8742i	0.650456	−	1.12662i	0.983012	−	0.183540i	$-0.0587557\pi$
$570$		0			0
$571$	29.6336			1.24013			0.620065	−	0.784551i	$-0.287106\pi$
$571$	29.6336			1.24013			0.620065	+	0.784551i	$0.287106\pi$
$572$	−8.00626	−	1.35395i	−0.334758	−	0.0566116i
$573$		−	8.71875i		−	0.364231i
$574$	9.25934	+	5.34589i	0.386478	+	0.223133i
$575$		0			0
$576$	4.19615	+	7.26795i	0.174840	+	0.302831i
$577$	−17.7788			−0.740140			−0.370070	−	0.929004i	$-0.620666\pi$
$577$	−17.7788			−0.740140			−0.370070	+	0.929004i	$0.620666\pi$
$578$	−7.42965	−	12.8685i	−0.309033	−	0.535260i
$579$	−5.58869	+	3.22663i	−0.232258	+	0.134094i
$580$		0			0
$581$	9.97052	+	17.2695i	0.413647	+	0.716458i
$582$	4.67848	+	2.70112i	0.193929	+	0.111965i
$583$	16.3923	−	28.3923i	0.678900	−	1.17589i
$584$	−34.1790			−1.41434
$585$		0			0
$586$	19.0959			0.788846
$587$	2.78102	−	4.81687i	0.114785	−	0.198814i	−0.802909	−	0.596102i	$-0.796715\pi$
$587$	2.78102	−	4.81687i	0.114785	−	0.198814i	0.917694	+	0.397288i	$0.130049\pi$
$588$	−0.740888	−	0.427752i	−0.0305537	−	0.0176402i
$589$	11.6978	+	20.2612i	0.482001	+	0.834850i
$590$		0			0
$591$	10.0399	−	5.79651i	0.412984	−	0.238437i
$592$	−8.25207	−	14.2930i	−0.339158	−	0.587439i
$593$	33.4290			1.37276			0.686382	−	0.727241i	$-0.259198\pi$
$593$	33.4290			1.37276			0.686382	+	0.727241i	$0.259198\pi$
$594$	1.73205	+	3.00000i	0.0710669	+	0.123091i
$595$		0			0
$596$	−4.32644	−	2.49787i	−0.177218	−	0.102317i
$597$		−	0.801382i		−	0.0327984i
$598$	−12.4440	−	33.4583i	−0.508871	−	1.36821i
$599$	8.14349			0.332734			0.166367	−	0.986064i	$-0.446796\pi$
$599$	8.14349			0.332734			0.166367	+	0.986064i	$0.446796\pi$
$600$		0			0
$601$	−11.5588	+	20.0204i	−0.471494	+	0.816651i	−0.999468	−	0.0326092i	$-0.989618\pi$
$601$	−11.5588	+	20.0204i	−0.471494	+	0.816651i	0.527974	+	0.849260i	$0.322952\pi$
$602$	−26.6080	+	15.3621i	−1.08446	+	0.626113i
$603$	−5.87855			−0.239393
$604$	−8.03945	+	4.64158i	−0.327121	+	0.188863i
$605$		0			0
$606$			3.14450i			0.127736i
$607$	−6.03361	+	3.48351i	−0.244897	+	0.141391i	−0.617425	−	0.786629i	$-0.711824\pi$
$607$	−6.03361	+	3.48351i	−0.244897	+	0.141391i	0.372528	+	0.928021i	$0.378491\pi$
$608$	25.0679	+	14.4729i	1.01664	+	0.586955i
$609$	16.5401	+	9.54942i	0.670238	+	0.386962i
$610$		0			0
$611$	−1.08072	+	6.39056i	−0.0437213	+	0.258535i
$612$		−	1.42775i		−	0.0577135i
$613$	17.1926	−	29.7784i	0.694401	−	1.20274i	−0.275982	−	0.961163i	$-0.589003\pi$
$613$	17.1926	−	29.7784i	0.694401	−	1.20274i	0.970382	−	0.241574i	$-0.0776638\pi$
$614$	8.78712	−	15.2197i	0.354620	−	0.614219i
$615$		0			0
$616$		−	27.0492i		−	1.08984i
$617$	−7.80446	−	13.5177i	−0.314196	−	0.544203i	0.665070	−	0.746781i	$-0.268402\pi$
$617$	−7.80446	−	13.5177i	−0.314196	−	0.544203i	−0.979266	+	0.202578i	$0.935068\pi$
$618$	4.70341	+	8.14655i	0.189199	+	0.327702i
$619$			16.0626i			0.645610i	0.946465	+	0.322805i	$0.104626\pi$
$619$			16.0626i			0.645610i	−0.946465	+	0.322805i	$0.895374\pi$
$620$		0			0
$621$	4.39627	−	7.61457i	0.176416	−	0.305562i
$622$	−14.0721	+	24.3735i	−0.564238	+	0.977290i
$623$			0.265947i			0.0106550i
$624$	−2.51376	−	6.75877i	−0.100631	−	0.270568i
$625$		0			0
$626$	−1.13234	−	0.653757i	−0.0452574	−	0.0261294i
$627$	19.7704	+	11.4144i	0.789554	+	0.455849i
$628$	5.06123	−	2.92210i	0.201965	−	0.116605i
$629$			16.0944i			0.641725i
$630$		0			0
$631$	−31.7588	+	18.3359i	−1.26430	+	0.729942i	−0.973903	−	0.226965i	$-0.927120\pi$
$631$	−31.7588	+	18.3359i	−1.26430	+	0.729942i	−0.290394	+	0.956907i	$0.593786\pi$
$632$	−34.1381			−1.35794
$633$	7.18116	−	4.14605i	0.285426	−	0.164791i
$634$	−4.85641	+	8.41154i	−0.192873	+	0.334065i
$635$		0			0
$636$	−7.80138			−0.309345
$637$	3.24670	+	2.68576i	0.128639	+	0.106414i
$638$			23.1485i			0.916458i
$639$	8.91942	+	5.14963i	0.352847	+	0.203716i
$640$		0			0
$641$	13.3211	+	23.0728i	0.526152	+	0.911322i	0.999536	+	0.0304659i	$0.00969909\pi$
$641$	13.3211	+	23.0728i	0.526152	+	0.911322i	−0.473384	+	0.880856i	$0.656968\pi$
$642$	−7.15097			−0.282226
$643$	−1.03048	−	1.78484i	−0.0406381	−	0.0703873i	0.844991	−	0.534781i	$-0.179606\pi$
$643$	−1.03048	−	1.78484i	−0.0406381	−	0.0703873i	−0.885629	+	0.464393i	$0.846272\pi$
$644$	−15.9317	+	9.19815i	−0.627796	+	0.362458i
$645$		0			0
$646$	8.14850	+	14.1136i	0.320598	+	0.555293i
$647$	13.4468	+	7.76353i	0.528649	+	0.305216i	0.740466	−	0.672093i	$-0.234605\pi$
$647$	13.4468	+	7.76353i	0.528649	+	0.305216i	−0.211817	+	0.977309i	$0.567938\pi$
$648$	1.53819	−	2.66422i	0.0604258	−	0.104661i
$649$	14.8222			0.581821
$650$		0			0
$651$	−9.01084			−0.353163
$652$	4.51023	−	7.81195i	0.176634	−	0.305940i
$653$	−35.3976	−	20.4368i	−1.38521	−	0.799754i	−0.392444	−	0.919776i	$-0.628370\pi$
$653$	−35.3976	−	20.4368i	−1.38521	−	0.799754i	−0.992771	+	0.120022i	$0.961703\pi$
$654$	6.64336	+	11.5066i	0.259776	+	0.449945i
$655$		0			0
$656$	5.75419	−	3.32218i	0.224663	−	0.129710i
$657$	5.55507	+	9.62167i	0.216724	+	0.375377i
$658$	−5.78517			−0.225530
$659$	0.917364	+	1.58892i	0.0357354	+	0.0618956i	0.883340	−	0.468733i	$-0.155289\pi$
$659$	0.917364	+	1.58892i	0.0357354	+	0.0618956i	−0.847605	+	0.530628i	$0.821956\pi$
$660$		0			0
$661$	15.0413	+	8.68408i	0.585038	+	0.337772i	0.763133	−	0.646242i	$-0.223660\pi$
$661$	15.0413	+	8.68408i	0.585038	+	0.337772i	−0.178095	+	0.984013i	$0.556994\pi$
$662$		−	28.8519i		−	1.12136i
$663$	−1.17256	+	6.93362i	−0.0455384	+	0.269280i
$664$	21.4641			0.832969
$665$		0			0
$666$	−4.64605	+	8.04719i	−0.180031	+	0.311822i
$667$	50.8836	−	29.3776i	1.97022	−	1.13751i
$668$	−16.0624			−0.621472
$669$	−11.0517	+	6.38068i	−0.427282	+	0.246691i
$670$		0			0
$671$		−	19.2826i		−	0.744396i
$672$	−9.65488	+	5.57425i	−0.372445	+	0.215031i
$673$	−8.23410	−	4.75396i	−0.317401	−	0.183252i	0.332832	−	0.942986i	$-0.391996\pi$
$673$	−8.23410	−	4.75396i	−0.317401	−	0.183252i	−0.650234	+	0.759734i	$0.725329\pi$
$674$	−19.6761	−	11.3600i	−0.757894	−	0.437570i
$675$		0			0
$676$	−1.78371	−	9.34801i	−0.0686041	−	0.359539i
$677$		−	20.7375i		−	0.797008i	−0.917167	−	0.398504i	$-0.869530\pi$
$677$		−	20.7375i		−	0.797008i	0.917167	−	0.398504i	$-0.130470\pi$
$678$	−1.95035	+	3.37810i	−0.0749026	+	0.129735i
$679$	−6.85596	+	11.8749i	−0.263107	+	0.455715i
$680$		0			0
$681$			17.1114i			0.655709i
$682$	−5.46073	−	9.45827i	−0.209102	−	0.362176i
$683$	8.34393	+	14.4521i	0.319272	+	0.552995i	0.980336	−	0.197334i	$-0.0632284\pi$
$683$	8.34393	+	14.4521i	0.319272	+	0.552995i	−0.661065	+	0.750329i	$0.729895\pi$
$684$		−	5.43233i		−	0.207710i
$685$		0			0
$686$	9.38352	−	16.2527i	0.358264	−	0.620532i
$687$	3.19996	−	5.54250i	0.122086	−	0.211460i
$688$			19.0935i			0.727932i
$689$	37.8860	+	6.40698i	1.44334	+	0.244086i
$690$		0			0
$691$	19.6119	+	11.3229i	0.746073	+	0.430745i	0.824273	−	0.566192i	$-0.191584\pi$
$691$	19.6119	+	11.3229i	0.746073	+	0.430745i	−0.0782005	+	0.996938i	$0.524917\pi$
$692$	−9.54167	−	5.50889i	−0.362720	−	0.209416i
$693$	−7.61457	+	4.39627i	−0.289253	+	0.167001i
$694$		−	27.2429i		−	1.03413i
$695$		0			0
$696$	17.8034	−	10.2788i	0.674836	−	0.389616i
$697$	−6.47941			−0.245425
$698$	25.0387	−	14.4561i	0.947728	−	0.547171i
$699$	0.335778	−	0.581585i	0.0127003	−	0.0219976i
$700$		0			0
$701$	−9.33818			−0.352698			−0.176349	−	0.984328i	$-0.556429\pi$
$701$	−9.33818			−0.352698			−0.176349	+	0.984328i	$0.556429\pi$
$702$	−2.58784	+	3.12832i	−0.0976719	+	0.118071i
$703$			61.2361i			2.30956i
$704$	−22.3590	−	12.9090i	−0.842685	−	0.486524i
$705$		0			0
$706$	4.41691	+	7.65032i	0.166233	+	0.287923i
$707$	−7.98133			−0.300169
$708$	−1.76353	−	3.05452i	−0.0662775	−	0.114796i
$709$	−24.6318	+	14.2212i	−0.925068	+	0.534088i	−0.885248	−	0.465119i	$-0.846012\pi$
$709$	−24.6318	+	14.2212i	−0.925068	+	0.534088i	−0.0398194	+	0.999207i	$0.512678\pi$
$710$		0			0
$711$	5.54842	+	9.61015i	0.208082	+	0.360409i
$712$	0.247908	+	0.143130i	0.00929075	+	0.00536402i
$713$	−13.8604	+	24.0069i	−0.519075	+	0.899064i
$714$	−6.27679			−0.234903
$715$		0			0
$716$	0.351951			0.0131530
$717$	3.56491	−	6.17461i	0.133134	−	0.230595i
$718$	19.2250	+	11.0996i	0.717472	+	0.414233i
$719$	−15.9484	−	27.6235i	−0.594776	−	1.03018i	−0.993578	−	0.113145i	$-0.963907\pi$
$719$	−15.9484	−	27.6235i	−0.594776	−	1.03018i	0.398802	−	0.917037i	$-0.369426\pi$
$720$		0			0
$721$	−20.6775	+	11.9381i	−0.770070	+	0.444600i
$722$	20.3062	+	35.1714i	0.755720	+	1.30894i
$723$	−26.9383			−1.00184
$724$	−0.680394	−	1.17848i	−0.0252867	−	0.0437978i
$725$		0			0
$726$	1.49777	+	0.864736i	0.0555873	+	0.0320934i
$727$		−	4.68029i		−	0.173583i	−0.996227	−	0.0867913i	$-0.972339\pi$
$727$		−	4.68029i		−	0.173583i	0.996227	−	0.0867913i	$-0.0276613\pi$
$728$	29.7134	−	11.0512i	1.10125	−	0.409583i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	9.30972	−	16.1249i	0.344332	−	0.596401i
$732$	−3.97372	+	2.29423i	−0.146873	+	0.0847971i
$733$	−14.1306			−0.521926			−0.260963	−	0.965349i	$-0.584040\pi$
$733$	−14.1306			−0.521926			−0.260963	+	0.965349i	$0.584040\pi$
$734$	10.8986	−	6.29233i	0.402276	−	0.232254i
$735$		0			0
$736$			34.2970i			1.26420i
$737$	15.6618	−	9.04232i	0.576908	−	0.333078i
$738$	−3.23970	−	1.87044i	−0.119255	−	0.0688520i
$739$	10.2955	+	5.94409i	0.378725	+	0.218657i	0.677263	−	0.735741i	$-0.263166\pi$
$739$	10.2955	+	5.94409i	0.378725	+	0.218657i	−0.298539	+	0.954398i	$0.596499\pi$
$740$		0			0
$741$	−4.46137	+	26.3812i	−0.163892	+	0.969136i
$742$			34.2970i			1.25908i
$743$	−12.0050	+	20.7932i	−0.440420	+	0.762830i	−0.997721	−	0.0674812i	$-0.978504\pi$
$743$	−12.0050	+	20.7932i	−0.440420	+	0.762830i	0.557301	+	0.830311i	$0.311837\pi$
$744$	−4.84953	+	8.39964i	−0.177793	+	0.307946i
$745$		0			0
$746$		−	9.85473i		−	0.360807i
$747$	−3.48853	−	6.04232i	−0.127639	−	0.221077i
$748$	2.19615	+	3.80385i	0.0802993	+	0.139082i
$749$		−	18.1505i		−	0.663205i
$750$		0			0
$751$	7.93491	−	13.7437i	0.289549	−	0.501513i	−0.684153	−	0.729338i	$-0.739828\pi$
$751$	7.93491	−	13.7437i	0.289549	−	0.501513i	0.973702	+	0.227825i	$0.0731614\pi$
$752$	−1.79759	+	3.11352i	−0.0655513	+	0.113538i
$753$		−	11.6480i		−	0.424478i
$754$	−25.4285	+	9.45750i	−0.926052	+	0.344422i
$755$		0			0
$756$	1.81195	+	1.04613i	0.0659001	+	0.0380474i
$757$	31.3188	+	18.0819i	1.13830	+	0.657198i	0.946009	−	0.324140i	$-0.105075\pi$
$757$	31.3188	+	18.0819i	1.13830	+	0.657198i	0.192291	+	0.981338i	$0.438408\pi$
$758$	−18.3036	+	10.5676i	−0.664817	+	0.383832i
$759$			27.0492i			0.981823i
$760$		0			0
$761$	−12.6597	+	7.30905i	−0.458912	+	0.264953i	−0.711587	−	0.702598i	$-0.752023\pi$
$761$	−12.6597	+	7.30905i	−0.458912	+	0.264953i	0.252675	+	0.967551i	$0.418690\pi$
$762$	−16.8590			−0.610737
$763$	−29.2060	+	16.8621i	−1.05733	+	0.610449i
$764$	3.19128	−	5.52746i	0.115457	−	0.199977i
$765$		0			0
$766$	−6.84029			−0.247150
$767$	6.05571	+	16.2821i	0.218659	+	0.587912i
$768$			14.9282i			0.538675i
$769$	15.8994	+	9.17950i	0.573346	+	0.331021i	0.758484	−	0.651691i	$-0.225940\pi$
$769$	15.8994	+	9.17950i	0.573346	+	0.331021i	−0.185139	+	0.982712i	$0.559273\pi$
$770$		0			0
$771$	3.63939	+	6.30362i	0.131070	+	0.227019i
$772$	−4.72412			−0.170025
$773$	−4.26519	−	7.38753i	−0.153408	−	0.265711i	0.779070	−	0.626937i	$-0.215692\pi$
$773$	−4.26519	−	7.38753i	−0.153408	−	0.265711i	−0.932478	+	0.361226i	$0.882358\pi$
$774$	9.30972	−	5.37497i	0.334631	−	0.193199i
$775$		0			0
$776$	7.37960	+	12.7818i	0.264912	+	0.458841i
$777$	−20.4253	−	11.7925i	−0.732753	−	0.423055i
$778$	5.44196	−	9.42575i	0.195104	−	0.337930i
$779$	−24.6530			−0.883284
$780$		0			0
$781$	−31.6844			−1.13376
$782$	−9.65488	+	16.7227i	−0.345258	+	0.598004i
$783$	−5.78712	−	3.34120i	−0.206815	−	0.119405i
$784$	1.16864	+	2.02414i	0.0417371	+	0.0722909i
$785$		0			0
$786$	10.3203	−	5.95845i	0.368114	−	0.212531i
$787$	1.71288	+	2.96679i	0.0610574	+	0.105755i	0.894938	−	0.446190i	$-0.147219\pi$
$787$	1.71288	+	2.96679i	0.0610574	+	0.105755i	−0.833881	+	0.551944i	$0.813886\pi$
$788$	8.48668			0.302326
$789$	−11.9639	−	20.7220i	−0.425925	−	0.737724i
$790$		0			0
$791$	−8.57425	−	4.95035i	−0.304865	−	0.176014i
$792$			9.46410i			0.336292i
$793$	21.1818	−	7.87805i	0.752189	−	0.279758i
$794$	27.3982			0.972327
$795$		0			0
$796$	0.293326	−	0.508056i	0.0103967	−	0.0180076i
$797$	24.3361	−	14.0505i	0.862030	−	0.497693i	−0.00266150	−	0.999996i	$-0.500847\pi$
$797$	24.3361	−	14.0505i	0.862030	−	0.497693i	0.864692	+	0.502303i	$0.167514\pi$
$798$	−23.8820			−0.845414
$799$	3.03622	−	1.75296i	0.107414	−	0.0620153i
$800$		0			0
$801$		−	0.0930509i		−	0.00328779i
$802$	8.67556	−	5.00884i	0.306345	−	0.176868i
$803$	−29.5999	−	17.0895i	−1.04456	−	0.603076i
$804$	−3.72685	−	2.15170i	−0.131436	−	0.0758845i
$805$		0			0
$806$	8.15884	−	9.86284i	0.287383	−	0.347404i
$807$			4.38147i			0.154235i
$808$	−4.29546	+	7.43996i	−0.151114	+	0.261737i
$809$	18.0846	−	31.3235i	0.635822	−	1.10128i	−0.350518	−	0.936556i	$-0.613995\pi$
$809$	18.0846	−	31.3235i	0.635822	−	1.10128i	0.986340	−	0.164720i	$-0.0526721\pi$
$810$		0			0
$811$		−	13.9825i		−	0.490993i	−0.969397	−	0.245497i	$-0.921049\pi$
$811$		−	13.9825i		−	0.490993i	0.969397	−	0.245497i	$-0.0789510\pi$
$812$	6.99066	+	12.1082i	0.245324	+	0.424914i
$813$	−1.24412	−	2.15488i	−0.0436333	−	0.0755751i
$814$		−	28.5860i		−	1.00194i
$815$		0			0
$816$	−1.95035	+	3.37810i	−0.0682757	+	0.118257i
$817$	35.4218	−	61.3523i	1.23925	−	2.14645i
$818$		−	31.8540i		−	1.11375i
$819$	−7.94028	−	6.56844i	−0.277456	−	0.229520i
$820$		0			0
$821$	3.67156	+	2.11977i	0.128138	+	0.0739806i	0.562699	−	0.826662i	$-0.309763\pi$
$821$	3.67156	+	2.11977i	0.128138	+	0.0739806i	−0.434561	+	0.900643i	$0.643096\pi$
$822$	8.49038	+	4.90192i	0.296136	+	0.170974i
$823$	−29.1332	+	16.8201i	−1.01552	+	0.586310i	−0.912803	−	0.408400i	$-0.866087\pi$
$823$	−29.1332	+	16.8201i	−1.01552	+	0.586310i	−0.102716	+	0.994711i	$0.532753\pi$
$824$			25.6999i			0.895299i
$825$		0			0
$826$	−13.4285	+	7.75296i	−0.467238	+	0.269760i
$827$	−6.94609			−0.241539			−0.120770	−	0.992681i	$-0.538536\pi$
$827$	−6.94609			−0.241539			−0.120770	+	0.992681i	$0.538536\pi$
$828$	5.57425	−	3.21829i	0.193719	−	0.111843i
$829$	−6.68271	+	11.5748i	−0.232100	+	0.402009i	−0.958426	−	0.285341i	$-0.907893\pi$
$829$	−6.68271	+	11.5748i	−0.232100	+	0.402009i	0.726326	+	0.687351i	$0.241226\pi$
$830$		0			0
$831$	−21.7061			−0.752975
$832$	5.04550	−	29.8353i	0.174921	−	1.03435i
$833$		−	2.27925i		−	0.0789714i
$834$	11.3675	+	6.56302i	0.393624	+	0.227259i
$835$		0			0
$836$	8.35596	+	14.4729i	0.288997	+	0.500557i
$837$	3.15276			0.108975
$838$	16.2682	+	28.1774i	0.561976	+	0.973371i
$839$	−17.3830	+	10.0361i	−0.600127	+	0.346483i	−0.769091	−	0.639139i	$-0.779291\pi$
$839$	−17.3830	+	10.0361i	−0.600127	+	0.346483i	0.168965	+	0.985622i	$0.445958\pi$
$840$		0			0
$841$	−7.82721	−	13.5571i	−0.269904	−	0.467487i
$842$	−11.7152	−	6.76375i	−0.403731	−	0.233094i
$843$	14.8635	−	25.7443i	0.511926	−	0.886682i
$844$	6.07023			0.208946
$845$		0			0
$846$	2.02414			0.0695915
$847$	−2.19486	+	3.80161i	−0.0754164	+	0.130625i
$848$	18.4583	+	10.6569i	0.633860	+	0.365959i
$849$	13.9998	+	24.2483i	0.480471	+	0.832200i
$850$		0			0
$851$	−62.8359	+	36.2783i	−2.15399	+	1.24360i
$852$	3.76979	+	6.52947i	0.129151	+	0.223696i
$853$	54.6353			1.87068			0.935338	−	0.353755i	$-0.115095\pi$
$853$	54.6353			1.87068			0.935338	+	0.353755i	$0.115095\pi$
$854$	10.0861	+	17.4696i	0.345138	+	0.597796i
$855$		0			0
$856$	−16.9194	−	9.76840i	−0.578292	−	0.333877i
$857$		−	3.66436i		−	0.125172i	−0.998040	−	0.0625860i	$-0.980065\pi$
$857$		−	3.66436i		−	0.125172i	0.998040	−	0.0625860i	$-0.0199348\pi$
$858$	2.08264	−	12.3151i	0.0711000	−	0.420432i
$859$	−28.1460			−0.960330			−0.480165	−	0.877178i	$-0.659423\pi$
$859$	−28.1460			−0.960330			−0.480165	+	0.877178i	$0.659423\pi$
$860$		0			0
$861$	4.74754	−	8.22298i	0.161796	−	0.280238i
$862$	−22.4513	+	12.9623i	−0.764696	+	0.441497i
$863$	50.4623			1.71776			0.858878	−	0.512180i	$-0.171162\pi$
$863$	50.4623			1.71776			0.858878	+	0.512180i	$0.171162\pi$
$864$	3.37810	−	1.95035i	0.114925	−	0.0663521i
$865$		0			0
$866$			30.2671i			1.02852i
$867$	−11.4282	+	6.59808i	−0.388122	+	0.224082i
$868$	−5.71264	−	3.29820i	−0.193900	−	0.111948i
$869$	−29.5644	−	17.0690i	−1.00291	−	0.579028i
$870$		0			0
$871$	16.3317	+	13.5101i	0.553378	+	0.457771i
$872$			36.3000i			1.22927i
$873$	2.39879	−	4.15483i	0.0811869	−	0.140620i
$874$	−36.7351	+	63.6270i	−1.24258	+	2.15221i
$875$		0			0
$876$			8.13319i			0.274795i
$877$	11.6043	+	20.0993i	0.391851	+	0.678705i	0.992694	−	0.120662i	$-0.0385016\pi$
$877$	11.6043	+	20.0993i	0.391851	+	0.678705i	−0.600843	+	0.799367i	$0.705168\pi$
$878$	17.8220	+	30.8685i	0.601462	+	1.04176i
$879$		−	16.9586i		−	0.572000i
$880$		0			0
$881$	−8.55758	+	14.8222i	−0.288312	+	0.499371i	−0.973407	−	0.229083i	$-0.926427\pi$
$881$	−8.55758	+	14.8222i	−0.288312	+	0.499371i	0.685095	+	0.728454i	$0.259761\pi$
$882$	0.657963	−	1.13963i	0.0221548	−	0.0383732i
$883$			21.3589i			0.718783i	0.933187	+	0.359391i	$0.117016\pi$
$883$			21.3589i			0.718783i	−0.933187	+	0.359391i	$0.882984\pi$
$884$	−3.28125	+	3.96655i	−0.110361	+	0.133410i
$885$		0			0
$886$	9.65355	+	5.57348i	0.324317	+	0.187245i
$887$	29.7220	+	17.1600i	0.997968	+	0.576177i	0.907646	−	0.419735i	$-0.137877\pi$
$887$	29.7220	+	17.1600i	0.997968	+	0.576177i	0.0903216	+	0.995913i	$0.471210\pi$
$888$	−21.9853	+	12.6932i	−0.737779	+	0.425957i
$889$		−	42.7913i		−	1.43517i
$890$		0			0
$891$	2.66422	−	1.53819i	0.0892548	−	0.0515313i
$892$	−9.34196			−0.312792
$893$	11.5522	−	6.66969i	0.386581	−	0.223193i
$894$	3.84220	−	6.65488i	0.128502	−	0.222573i
$895$		0			0
$896$	4.71191			0.157414
$897$	−29.7134	+	11.0512i	−0.992102	+	0.368987i
$898$			16.8998i			0.563953i
$899$	18.2454	+	10.5340i	0.608518	+	0.351328i
$900$		0			0
$901$	−10.3923	−	18.0000i	−0.346218	−	0.599667i
$902$	11.5084			0.383187
$903$	13.6427	+	23.6298i	0.454000	+	0.786351i
$904$	−9.22913	+	5.32844i	−0.306956	+	0.177221i
$905$		0			0
$906$	−7.13963	−	12.3662i	−0.237198	−	0.410839i
$907$	−51.0161	−	29.4542i	−1.69396	−	0.978010i	−0.951261	−	0.308387i	$-0.900211\pi$
$907$	−51.0161	−	29.4542i	−1.69396	−	0.978010i	−0.742701	−	0.669623i	$-0.766456\pi$
$908$	−6.26319	+	10.8482i	−0.207851	+	0.360009i
$909$	2.79254			0.0926229
$910$		0			0
$911$	−55.5007			−1.83882			−0.919410	−	0.393299i	$-0.871334\pi$
$911$	−55.5007			−1.83882			−0.919410	+	0.393299i	$0.871334\pi$
$912$	−7.42071	+	12.8530i	−0.245724	+	0.425607i
$913$	18.5885	+	10.7321i	0.615188	+	0.355179i
$914$	−7.33633	−	12.7069i	−0.242664	−	0.420307i
$915$		0			0
$916$	4.05739	−	2.34254i	0.134060	−	0.0773996i
$917$	15.1237	+	26.1950i	0.499428	+	0.865034i
$918$	2.19615			0.0724838
$919$	27.3656	+	47.3985i	0.902707	+	1.56353i	0.823967	+	0.566638i	$0.191756\pi$
$919$	27.3656	+	47.3985i	0.902707	+	1.56353i	0.0787401	+	0.996895i	$0.474910\pi$
$920$		0			0
$921$	−13.5163	−	7.80362i	−0.445376	−	0.257138i
$922$			32.3358i			1.06492i
$923$	−12.9449	−	34.8052i	−0.426087	−	1.14563i
$924$	−6.43659			−0.211748
$925$		0			0
$926$	−0.259162	+	0.448881i	−0.00851658	+	0.0147511i
$927$	7.23474	−	4.17698i	0.237620	−	0.137190i
$928$	26.0660			0.855657
$929$	−14.8799	+	8.59092i	−0.488194	+	0.281859i	−0.723825	−	0.689984i	$-0.757618\pi$
$929$	−14.8799	+	8.59092i	−0.488194	+	0.281859i	0.235631	+	0.971843i	$0.424284\pi$
$930$		0			0
$931$		−	8.67213i		−	0.284218i
$932$	0.425750	−	0.245807i	0.0139459	−	0.00805167i
$933$	21.6455	+	12.4970i	0.708642	+	0.409135i
$934$	33.2177	+	19.1782i	1.08692	+	0.627531i
$935$		0			0
$936$	−10.3963	+	3.86663i	−0.339813	+	0.126385i
$937$		−	39.6401i		−	1.29499i	−0.762071	−	0.647493i	$-0.775817\pi$
$937$		−	39.6401i		−	1.29499i	0.762071	−	0.647493i	$-0.224183\pi$
$938$	−9.45945	+	16.3842i	−0.308862	+	0.534965i
$939$	−0.580584	+	1.00560i	−0.0189467	+	0.0328166i
$940$		0			0
$941$			33.3796i			1.08815i	0.839038	+	0.544073i	$0.183118\pi$
$941$			33.3796i			1.08815i	−0.839038	+	0.544073i	$0.816882\pi$
$942$	4.49474	+	7.78512i	0.146447	+	0.253653i
$943$	−14.6052	−	25.2970i	−0.475612	−	0.823784i
$944$			9.63611i			0.313629i
$945$		0			0
$946$	−16.5354	+	28.6402i	−0.537613	+	0.931174i
$947$	−10.2800	+	17.8054i	−0.334054	+	0.578599i	−0.983303	−	0.181978i	$-0.941750\pi$
$947$	−10.2800	+	17.8054i	−0.334054	+	0.578599i	0.649249	+	0.760576i	$0.275084\pi$
$948$			8.12345i			0.263837i
$949$	6.67948	−	39.4974i	0.216825	−	1.28214i
$950$		0			0
$951$	7.47007	+	4.31285i	0.242234	+	0.139854i
$952$	−14.8510	−	8.57425i	−0.481325	−	0.277893i
$953$	47.5234	−	27.4376i	1.53943	−	0.888792i	0.540561	−	0.841305i	$-0.318212\pi$
$953$	47.5234	−	27.4376i	1.53943	−	0.888792i	0.998872	−	0.0474871i	$-0.0151213\pi$
$954$		−	12.0000i		−	0.388514i
$955$		0			0
$956$	4.52013	−	2.60970i	0.146191	−	0.0844036i
$957$	20.5576			0.664532
$958$	30.1632	−	17.4147i	0.974528	−	0.562644i
$959$	−12.4420	+	21.5502i	−0.401773	+	0.695892i
$960$		0			0
$961$	21.0601			0.679359
$962$	31.4016	−	11.6790i	1.01243	−	0.376547i
$963$			6.35059i			0.204645i
$964$	−17.0782	−	9.86009i	−0.550051	−	0.317572i
$965$		0			0
$966$	−14.1485	−	24.5059i	−0.455221	−	0.788465i
$967$	10.9215			0.351211			0.175605	−	0.984461i	$-0.443812\pi$
$967$	10.9215			0.351211			0.175605	+	0.984461i	$0.443812\pi$
$968$	2.36250	+	4.09197i	0.0759337	+	0.131521i
$969$	12.5339	−	7.23647i	0.402648	−	0.232469i
$970$		0			0
$971$	−15.7356	−	27.2548i	−0.504978	−	0.874648i	−0.999983	−	0.00575765i	$-0.998167\pi$
$971$	−15.7356	−	27.2548i	−0.504978	−	0.874648i	0.495005	−	0.868890i	$-0.335166\pi$
$972$	−0.633975	−	0.366025i	−0.0203347	−	0.0117403i
$973$	−16.6582	+	28.8528i	−0.534037	+	0.924979i
$974$	18.6223			0.596698
$975$		0			0
$976$	12.5359			0.401264
$977$	−15.7767	+	27.3260i	−0.504740	+	0.874235i	0.495245	+	0.868753i	$0.335078\pi$
$977$	−15.7767	+	27.3260i	−0.504740	+	0.874235i	−0.999985	+	0.00548205i	$0.998255\pi$
$978$	12.0163	+	6.93759i	0.384238	+	0.221840i
$979$	0.143130	+	0.247908i	0.00457445	+	0.00792318i
$980$		0			0
$981$	10.2187	−	5.89980i	0.326259	−	0.188366i
$982$	10.5185	+	18.2186i	0.335659	+	0.581378i
$983$	43.6214			1.39131			0.695654	−	0.718377i	$-0.255115\pi$
$983$	43.6214			1.39131			0.695654	+	0.718377i	$0.255115\pi$
$984$	−5.11015	−	8.85104i	−0.162906	−	0.282161i
$985$		0			0
$986$	12.7094	+	7.33778i	0.404750	+	0.233683i
$987$			5.13766i			0.163534i
$988$	−12.4846	+	15.0920i	−0.397187	+	0.480141i
$989$	83.9401			2.66914
$990$		0			0
$991$	−8.99740	+	15.5840i	−0.285812	+	0.495041i	−0.972806	−	0.231623i	$-0.925597\pi$
$991$	−8.99740	+	15.5840i	−0.285812	+	0.495041i	0.686994	+	0.726663i	$0.258930\pi$
$992$	−10.6503	+	6.14896i	−0.338148	+	0.195230i
$993$	−25.6227			−0.813110
$994$	28.7053	−	16.5730i	0.910477	−	0.525664i
$995$		0			0
$996$		−	5.10757i		−	0.161840i
$997$	20.9657	−	12.1045i	0.663990	−	0.383355i	−0.129806	−	0.991539i	$-0.541435\pi$
$997$	20.9657	−	12.1045i	0.663990	−	0.383355i	0.793796	+	0.608185i	$0.208102\pi$
$998$	10.7236	+	6.19128i	0.339450	+	0.195982i
$999$	7.14650	+	4.12603i	0.226105	+	0.130542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.h.199.2		8
5.2	odd	4		195.2.bb.b.121.2	✓	8
5.3	odd	4		975.2.bc.j.901.3		8
5.4	even	2		975.2.w.i.199.3		8
13.10	even	6		975.2.w.i.49.3		8
15.2	even	4		585.2.bu.d.316.3		8
65.7	even	12		2535.2.a.bk.1.2		4
65.23	odd	12		975.2.bc.j.751.3		8
65.32	even	12		2535.2.a.bj.1.3		4
65.49	even	6	inner	975.2.w.h.49.2		8
65.62	odd	12		195.2.bb.b.166.2	yes	8
195.32	odd	12		7605.2.a.ci.1.2		4
195.62	even	12		585.2.bu.d.361.3		8
195.137	odd	12		7605.2.a.ch.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.2	✓	8	5.2	odd	4
195.2.bb.b.166.2	yes	8	65.62	odd	12
585.2.bu.d.316.3		8	15.2	even	4
585.2.bu.d.361.3		8	195.62	even	12
975.2.w.h.49.2		8	65.49	even	6	inner
975.2.w.h.199.2		8	1.1	even	1	trivial
975.2.w.i.49.3		8	13.10	even	6
975.2.w.i.199.3		8	5.4	even	2
975.2.bc.j.751.3		8	65.23	odd	12
975.2.bc.j.901.3		8	5.3	odd	4
2535.2.a.bj.1.3		4	65.32	even	12
2535.2.a.bk.1.2		4	65.7	even	12
7605.2.a.ch.1.3		4	195.137	odd	12
7605.2.a.ci.1.2		4	195.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.563016 + 0.975173i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(-0.975173 + 0.563016i) q^{6} +(-1.42904 - 2.47517i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.563016 + 0.975173i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(-0.975173 + 0.563016i) q^{6} +(-1.42904 - 2.47517i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.66422 - 1.53819i) q^{11} +0.732051i q^{12} +(0.601205 - 3.55507i) q^{13} +3.21829 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.68905 + 0.975173i) q^{17} -1.12603 q^{18} +(-6.42652 + 3.71035i) q^{19} -2.85808i q^{21} +(3.00000 - 1.73205i) q^{22} +(-7.61457 - 4.39627i) q^{23} +(-2.66422 - 1.53819i) q^{24} +(3.12832 + 2.58784i) q^{26} +1.00000i q^{27} +(1.04613 - 1.81195i) q^{28} +(-3.34120 + 5.78712i) q^{29} -3.15276i q^{31} +(-1.95035 - 3.37810i) q^{32} +(-1.53819 - 2.66422i) q^{33} -2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(4.12603 - 7.14650i) q^{37} -8.35596i q^{38} +(2.29820 - 2.77818i) q^{39} +(2.87710 + 1.66109i) q^{41} +(2.78712 + 1.60915i) q^{42} +(-8.26772 + 4.77337i) q^{43} -2.25207i q^{44} +(8.57425 - 4.95035i) q^{46} -1.79759 q^{47} +(1.73205 - 1.00000i) q^{48} +(-0.584320 + 1.01207i) q^{49} -1.95035 q^{51} +(2.47388 - 0.920099i) q^{52} +10.6569i q^{53} +(-0.975173 - 0.563016i) q^{54} +(4.39627 + 7.61457i) q^{56} -7.42071 q^{57} +(-3.76230 - 6.51649i) q^{58} +(-4.17256 + 2.40903i) q^{59} +(3.13397 + 5.42820i) q^{61} +(3.07448 + 1.77505i) q^{62} +(1.42904 - 2.47517i) q^{63} +8.39230 q^{64} +3.46410 q^{66} +(-2.93927 + 5.09097i) q^{67} +(-1.23647 - 0.713876i) q^{68} +(-4.39627 - 7.61457i) q^{69} +(8.91942 - 5.14963i) q^{71} +(-1.53819 - 2.66422i) q^{72} +11.1101 q^{73} +(4.64605 + 8.04719i) q^{74} +(-4.70454 - 2.71617i) q^{76} +8.79254i q^{77} +(1.41529 + 3.80530i) q^{78} +11.0968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.23970 + 1.87044i) q^{82} -6.97707 q^{83} +(1.81195 - 1.04613i) q^{84} -10.7499i q^{86} +(-5.78712 + 3.34120i) q^{87} +(8.19615 + 4.73205i) q^{88} +(-0.0805845 - 0.0465255i) q^{89} +(-9.65857 + 3.59226i) q^{91} -6.43659i q^{92} +(1.57638 - 2.73037i) q^{93} +(1.01207 - 1.75296i) q^{94} -3.90069i q^{96} +(-2.39879 - 4.15483i) q^{97} +(-0.657963 - 1.13963i) q^{98} -3.07638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 4 * q^9	\( 8 q - 4 q^{4} + 4 q^{9} - 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} + 24 q^{22} - 24 q^{23} - 24 q^{26} + 12 q^{28} - 12 q^{29} + 4 q^{36} + 24 q^{37} + 4 q^{39} + 36 q^{41} - 12 q^{42} + 12 q^{43} - 48 q^{47} + 4 q^{49} + 12 q^{52} - 24 q^{57} + 12 q^{58} - 36 q^{59} + 32 q^{61} + 48 q^{62} - 16 q^{64} + 12 q^{67} + 36 q^{71} + 48 q^{73} + 24 q^{74} - 48 q^{76} + 12 q^{78} + 16 q^{79} - 4 q^{81} + 12 q^{82} - 12 q^{84} - 12 q^{87} + 24 q^{88} - 36 q^{89} - 12 q^{93} - 12 q^{94} - 36 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 4 * q^9 - 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 + 24 * q^22 - 24 * q^23 - 24 * q^26 + 12 * q^28 - 12 * q^29 + 4 * q^36 + 24 * q^37 + 4 * q^39 + 36 * q^41 - 12 * q^42 + 12 * q^43 - 48 * q^47 + 4 * q^49 + 12 * q^52 - 24 * q^57 + 12 * q^58 - 36 * q^59 + 32 * q^61 + 48 * q^62 - 16 * q^64 + 12 * q^67 + 36 * q^71 + 48 * q^73 + 24 * q^74 - 48 * q^76 + 12 * q^78 + 16 * q^79 - 4 * q^81 + 12 * q^82 - 12 * q^84 - 12 * q^87 + 24 * q^88 - 36 * q^89 - 12 * q^93 - 12 * q^94 - 36 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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